Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 9
105 practice questions
Topics covered
Practice questions
21–30 of 105
Question 21
3 marks · Easy
Answer and see the solution →The statement is: "The sum of any two even numbers is always even."
(a)[1 mark]Write an algebraic expression for two even numbers.
(b)[2 marks]Show algebraically that their sum must be even.
Question 22
3 marks · Easy
Answer and see the solution →The graphs below represent the equations and .
Values for \(y = x^2\) and \(y = x + 4\) x y = x^2 y = x + 4 -3 9 1 -2 4 2 -1 1 3 0 0 4 1 1 5 2 4 6 3 9 7 (a)[2 marks]From the table, write down the two values of where the graphs intersect.
(b)[1 mark]Give the corresponding value of at either point of intersection.
Question 23
1 mark · Easy
Answer and see the solution →State how you can check that your solutions to a pair of simultaneous equations are correct.
Question 24
2 marks · Easy
Answer and see the solution →Show, by using algebra, that the difference between two consecutive even numbers is always 2.
Question 25
2 marks · Normal
Answer and see the solution →Solve the simultaneous equations for :
Question 26
3 marks · Normal
Answer and see the solution →The graphs of y = x + 2 and y = x^2 – 2x are shown below.
Calculate the x-coordinates of the points where the graphs intersect.
Question 27
3 marks · Normal
Answer and see the solution →A student claims that all prime numbers are odd. Explain, giving a counter-example, whether this claim is true or false.
Question 28
4 marks · Normal
Answer and see the solution →Solve the following system of equations.
(a)[3 marks]Given y = x^2 + 1 and x + y = 7, find the two possible values of x.
(b)[1 mark]For one of the solutions in part (a), find the corresponding value of y.
Question 29
4 marks · Normal
Answer and see the solution →The table shows several points that lie on the graph of y = x^2 – 3x + 2.
Some values of y = x^2 – 3x + 2 x y 0 2 1 0 2 0 3 2 (a)[2 marks]Plot the points from the table on the axes below and draw a smooth curve through them.
Axes for y = x^2 – 3x + 2 (b)[2 marks]Use your graph to estimate the solutions to y = 0.
Question 30
2 marks · Normal
Answer and see the solution →Give a counter-example to show that the statement below is false:
The difference between two numbers is always less than their sum.